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    (Original post by Gregorius)
    Yes, very much so. Though I feel I must say that the brightest students these days are just as bright as the best in my day (back when dinosaurs roamed the earth).



    On the other hand, when I went up to Cambridge the first year was a huge jump over school mathematics - even taught to the level of the seventh term Oxbridge exams. One of the things that has changed is the size of that jump; I think it's finally sunk in with universities realizing that they really don't want to have good students drop out or fail so early through no great fault of their own.
    Would you agree that the brightest students aren't able to shine out as much as they have before? I mean, getting 3 A's or more was a notable feat back then especially with the syllabus being harder. Whereas now, quite a lot walk away with multiple A*'s to boot without too much bother, so there isn't much discrimination at the top?

    Can you elaborate on the 'huge jump' thing? As it is, the jump is described as being a horrid large one, how bad was it for you? :-)
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    This is the clash of the Titans of the Maths room!
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    (Original post by Gregorius)
    Yes, very much so. Though I feel I must say that the brightest students these days are just as bright as the best in my day (back when dinosaurs roamed the earth).
    I'm not sure from your posts how involved you are with Cambridge maths these days and therefore whether I'm teaching you to suck eggs, but last time I tried to look at how things had changed, the impression I got was that the content of the 1st 2 years hadn't changed that much in total, but that a lot less of it was examined in the first year. I certainly don't get the feeling that Part II is any easier than in my day (*).

    On the other hand, when I went up to Cambridge the first year was a huge jump over school mathematics - even taught to the level of the seventh term Oxbridge exams. One of the things that has changed is the size of that jump; I think it's finally sunk in with universities realizing that they really don't want to have good students drop out or fail so early through no great fault of their own.
    I seem to be really unusual in that I really didn't find part IA a big jump at all. I usually found IA questions fairly straightforward, with common enough themes that at least 4-5 questions a paper could be considered routine. (e.g. oh, it's a rank-nullity question where you need to do some talking about the matrix of the transform w.r.t. the basis constructed during the proof).

    And although I think I got a reasonably comfortable 11 in M/FM S-levels, I certainly don't think I did outstandingly well in them. I'm sure I'd have struggled more with STEP than IA, even if taking STEP at that point in my education.

    (*) I find (as I'm sure do many) that the "easier" the maths, the better I tend to remember it, and these days there's not much beyond IB I remember well at all, which may bias things a bit. But I don't think it's really an issue here.
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    (Original post by Zacken)
    Would you agree that the brightest students aren't able to shine out as much as they have before? I mean, getting 3 A's or more was a notable feat back then especially with the syllabus being harder. Whereas now, quite a lot walk away with multiple A*'s to boot without too much bother, so there isn't much discrimination at the top?
    If you're talking about A-levels, then this is clearly true. However, there are plenty of other exams (STEP, for example) that give the brightest the opportunity to shine.

    Can you elaborate on the 'huge jump' thing? As it is, the jump is described as being a horrid large one, how bad was it for you? :-)
    Painful. We were exposed to the conjunction of technical difficulty (facility in algebraic manipulation, for example) with a high level of abstraction. One of the things I really like about modern undergraduate mathematics courses is the concentration on motivating examples - this is something we lacked. If we wanted an example, we had to go off and dream it up ourselves.

    Textbooks are much better these days too! I'm reading Visual Complex Analysis" at the moment for fun; how I wish we had supporting materials like this when I was learning.
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    (Original post by Gregorius)
    If you're talking about A-levels, then this is clearly true. However, there are plenty of other exams (STEP, for example) that give the brightest the opportunity to shine.



    Painful. We were exposed to the conjunction of technical difficulty (facility in algebraic manipulation, for example) with a high level of abstraction. One of the things I really like about modern undergraduate mathematics courses is the concentration on motivating examples - this is something we lacked. If we wanted an example, we had to go off and dream it up ourselves.

    Textbooks are much better these days too! I'm reading Visual Complex Analysis" at the moment for fun; how I wish we had supporting materials like this when I was learning.
    Thanks for sharing your experience! :-)

    I've heard great things about that book! You may want to look up "Things to make and do in the fourth dimension" as well if you want some quirky maths and a break from all the serious maths.
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    (Original post by Zacken)
    Would you agree that the brightest students aren't able to shine out as much as they have before? I mean, getting 3 A's or more was a notable feat back then especially with the syllabus being harder. Whereas now, quite a lot walk away with multiple A*'s to boot without too much bother, so there isn't much discrimination at the top?
    Well, Oxford/Cambridge have their own exams, and I think that means there's been less change in those cases.

    The bigger change to my mind is that in my day getting AAB basically meant you would get into any other university with 90+% certainty. So for people with a realistic chance at Oxbridge Maths, you were basically just choosing where you'd go if you didn't get in. Heck, there were a fair number of people who knew Oxbridge was a long shot but were still confident of AAA and therefore getting into whereever was their 2nd choice.

    Judging from horror stories on TSR, that side of things looks a *lot* scarier now.
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    (Original post by TeeEm)
    This is the clash of the Titans of the Maths room!
    Ah look, we're just practicing for the mathematical component of the next round of the Glass Bead Game. Next thread will be about composing four part invertible counterpoint with rhythmic structure derived from the octal expansoin of various lesser known transcendental numbers.
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    (Original post by DFranklin)
    I'm not sure from your posts how involved you are with Cambridge maths these days and therefore whether I'm teaching you to suck eggs
    I'm at York University now, and not even in the maths department! But I keep an eye out for what is going on and I'm a parent of an undergrad there. Please don't think that I don't need to be taught how to suck eggs!

    but last time I tried to look at how things had changed, the impression I got was that the content of the 1st 2 years hadn't changed that much in total, but that a lot less of it was examined in the first year. I certainly don't get the feeling that Part II is any easier than in my day (*).
    I have dug out my “schedules” from 1977-8 to compare today’s IA course with that of a while ago.Here is what is done in the first year today…(numbers of leactures in brackets)

    Vectors and Matrices (24)
    Groups (24)
    Analysis I (24)
    Vector Calculus (24)
    Differential Equations (24)
    Probability (24)
    Numbers and Sets (24)
    Dynamics and Relativity (24)

    …and these are the courses from 1977-8.

    Analysis I (24)
    Analysis II (24)
    Algebra I (Groups) (24)
    Algebra II (Vector Spaces) (24)
    Probability and its Applications (24)
    Vector Calculus (24)
    Linear Systems (24)
    Newtonian Dynamics (16)
    Special Relativity (8)
    Electrodynamics (24)
    Potential Theory (12)

    There’s clearly a lot of similarity on the face of it, but there are differences. Today’s Analysis I seems to include the easier bits of the old Analysis I & II; today’s Groups corresponds to the old Algebra I; Vectors and Matrices to Algebra II; today’s Numbers and Sets was spread over Analysis I and Algebra I. Today’s Differential Equations is new. In contrast, we had Linear Systems (101 things to do with Green’s functions, Laplace & Fourier Transforms) and added a full course in Electrodynamics and a half course in Potential Theory together with a second course in Analysis. It’s difficult to do a comparison of the contents of courses with similar titles, but to give an example, in Algebra I we got as far as the Sylow theorems.

    As for Part II, it looks very similar, but there’s not quite as much analysis these days (e.g. The two courses Measure Theory and Probability Theory have been combined in to one these days).

    I seem to be really unusual in that I really didn't find part IA a big jump at all. I usually found IA questions fairly straightforward, with common enough themes that at least 4-5 questions a paper could be considered routine. (e.g. oh, it's a rank-nullity question where you need to do some talking about the matrix of the transform w.r.t. the basis constructed during the proof).
    I'd be the first to admit I'm a slow learner!
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    (Original post by Zacken)
    Thanks for sharing your experience! :-)

    I've heard great things about that book! You may want to look up "Things to make and do in the fourth dimension" as well if you want some quirky maths and a break from all the serious maths.
    I was thinking about getting that book for my son, who is coming up to fifteen...thanks for the recommendation.
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    (Original post by Gregorius)
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    What on earth is potential theory? :eek:

    It looks, on the face of things, that you had many more hours of lectures than students nowadays. How many supervisions/problem sheets did you tend to have back then?
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    (Original post by Gregorius)
    I have dug out my “schedules” from 1977-8 to compare today’s IA course with that of a while ago.Here is what is done in the first year today…(numbers of leactures in brackets)

    Vectors and Matrices (24)
    Groups (24)
    Analysis I (24)
    Vector Calculus (24)
    Differential Equations (24)
    Probability (24)
    Numbers and Sets (24)
    Dynamics and Relativity (24)

    …and these are the courses from 1977-8.

    Analysis I (24)
    Analysis II (24)
    Algebra I (Groups) (24)
    Algebra II (Vector Spaces) (24)
    Probability and its Applications (24)
    Vector Calculus (24)
    Linear Systems (24)
    Newtonian Dynamics (16)
    Special Relativity (8)
    Electrodynamics (24)
    Potential Theory (12)
    So, I think IA has changed significantly from when I did my "what's changed since I did the Tripos?" survey? I distinctly remember that some of the "missing" courses were still there, but not examined until part IB. I wondered how that would work out at the time, and I'm guessing the answer was "not well" - I suspect student motivation to study unexamined material wasn't terribly high...

    FWIW, I'm roughly 10 years after you , and our course was very close to yours. I think we may have lost 12 lectures of material relative to you, but basically not much.

    They'd also introduced "fast/slow" courses for some topics - the slow course would cover somewhat less material and there'd be one question on the "extra" fast course material. Of course in practice they'd removed material for the slow course rather than added it for the fast, but I think the difference in actual material was fairly small, it was more that the most "difficult" topics weren't covered (e.g. group actions, or the fiddly analysis tests that let you decide convergence *on* the radius of convergence).

    FWIW, the "fast" Algebra course in my day also did the Sylow theorems (though I'm not sure they were actually examinable).

    I really need to dig up my old notes etc...
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    (Original post by Zacken)
    It looks, on the face of things, that you had many more hours of lectures than students nowadays.
    10 years after Gregorius, we has 4 lectures a day, 6 days a week. Course content was pretty similar. Two supervisions a week IIRC (I have a feeling we may have had an extra supervision for probability but maybe only every other week).
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    (Original post by Zacken)
    This brings up an interesting point that I've been meaning to raise recently:

    A-Level syllabi have been shrinking, in terms of content, for the past twenty years or so - has first year uni material been shifted/shrinked as well to allocate for the reduction in the syllabi?

    Quite a few of the old timers post about how much more advanced their maths A-Level was back in their day and DFranklin mentioned that convolutions was in Cambridge first year, which is where my question comes from.
    You've had good insights already from Gregorius and DFranklin but here's my take on it.

    EDIT: Didn't realise this was going to be so long. Sorry, don't bother reading anything but the bold bits unless you're really bored!

    - Theoretical physics has become de-emphasised: I get the feeling that in the past, undergrads were essentially told "maths is very useful for all sorts of things but really the only use which is important is for physics". Thus electrodynamics, relativity and potential theory were core parts of the undergrad syllabus. These days the importance of computing (and hence algorithms, optimisation, "discrete maths") and statistics means that the syllabus has become more varied. This is definitely for the better because it means that maths degrees are more interesting (and more useful) for many more people. In addition, we are going through a shift in many disciplines where they are becoming more quantitative. For example, witness the rise of "mathematical biology options" in the undergrad syllabus.

    Cambridge still retains a formidable choice in theoretical physics options if that's your thing.

    - Universities have got foundation courses which introduces the concept of proofs: These days, most courses have a "foundations" course (e.g. Cambridge's Numbers & Sets or Imperial's Foundations of Analysis) which provides a gentle introduction to abstraction and rigour. In the past you would thrown into the deep end in learning abstract algebra or analysis at a fast pace, without really having any formal experience of constructing proofs. I don't believe A-levels were much better at requiring you to prove things in the past (someone correct me if I'm wrong).

    The UK is behind in this lack of emphasis on proofs around the A-level age. For example, the old Hong Kong A-level (HKALE) routinely asked you to prove things, meaning by the time you go to university it is more realistic to be thrown in the deep end.

    Spoiler:
    Show
    You can go too far, and the HKALE probably did because for a general exam at 18 it was hard. One paper I opened at random from the mid-80's was essentially the same as a question from the 2015 STEP II paper.


    - The UK A-level has become less good at teaching algebraic manipulation. This is despite the syllabus remaining similar for a very long time - without wanting to start a massive debate, fewer A-level exam questions require sustained algebraic manipulation than in the past. Thus methods courses in the first year have to start at a more elementary point and proceed slower than corresponding courses 20 years ago. This is one of the points of STEP in my view - being successful at STEP requires more sustained manipulation so courses requiring it or something similar can remain faster paced.

    - Oxbridge have moved away from their experiments of offering two types of mathematics degrees. Around the late 80's and 90's, both universities offered two "strands" in their degree. The first (called Mathematical Sciences at Oxford or Alternative A at Cambridge) was designed for students who would stop after three years and go into employment. The second (Mathematics at Oxford or Alternative B at Cambridge) was primarily for those students who would go on to do research. Their design was flawed because essentially it became a system of tiering by ability (similar to how you have Foundation and Higher tiers at GCSE Maths), which meant that if you were on course for a first you would likely take the "harder" option even if it was less relevant to what you wanted to do after university.

    Trying to cater to everyone (which is the right thing to do in my view) has meant that courses have shifted their content around. This is neither a good or bad thing - in my view, so long as you are taught core material at some point in your degree, it doesn't really matter when that is. These things shift around every 5 years or so - Oxford can't seem to resist tweaking the first two years of their degree - and has more to do with how internally the department want to teach material than anything else.

    - There have been massive developments in mathematical-related disciplines which need space in the first two years of a maths degree. The most obvious topical example is the rise of "Big Data" and data science fast becoming a separate discipline. Trying to analyse a huge set of data is very different from the "classical" statistical techniques (hypothesis testing, regression or generalised linear models, parameter estimation) and requires a very different skill set. Oxford for example has expanded their statistics course which is now called Statistics and Data Analysis.

    In a dynamic field like mathematics, these new areas will mean the syllabus of an undergraduate degree will continue to evolve to try to offer students exposure to all of the key areas. It's not all about A-levels becoming crap or dumbing down of courses.

    I don't think any university has the "best" structure for the first two years of their degrees absolutely nailed yet, but that is for another thread. Maybe I should start one...
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    (Original post by DFranklin)
    10 years after Gregorius, we has 4 lectures a day, 6 days a week. Course content was pretty similar. Two supervisions a week IIRC (I have a feeling we may have had an extra supervision for probability but maybe only every other week).
    4 lectures a day?! :eek:


    (Original post by shamika)
    You've had good insights already from Gregorius and DFranklin but here's my take on it..
    I ended up reading it all (the woes of having public holidays) and your take is pretty interesting, it paints a much more positive light on why the course content is shifting around and makes a ton of sense. I especially like the whole part of foundation courses becoming a thing, IIRC Warwick has one as well - I prefer that than being thrown in the deep end of an already deep pool.

    I didn't know that Oxbridge used to have two different 'strands' of maths degrees - that just sounds really weird. :eek: I'm glad it isn't in place anymore.

    Thanks for taking the time to write up all of that. :-)
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    (Original post by Zacken)
    What on earth is potential theory? :eek:

    It looks, on the face of things, that you had many more hours of lectures than students nowadays. How many supervisions/problem sheets did you tend to have back then?
    Wikipedia's as good as anything here.

    As far as we were concerned, it ended up being Poisson's equation, Laplace's equation, more Green's functions, various flavours of orthogonal polynomial series, more Fourier analysis, boundary value problems...
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    (Original post by Zacken)
    Thank you very much for this, I've read it and I'll try digesting it soon - re-reading and consulting diagrams at the same time.

    I must say, your explanations are very nice. Every time I see you post on a thread, I open it up to see if it's one of these such explanations - there was one you did explaining Huygen's principle beautifully and another with you explaining how Jacobian's were just stretching/compressing the axes in three dimensions, etc... They're really nice!
    Well, I'm glad that someone appreciates the exquisitely crafted monologues that I gift selflessly to the world. In fact, I usually write up such an explanation when I feel that I ought to explain something to myself that I half-remember or for which I can think of a nice intuitive explanation, and would like to have written down for future reference. So it's as much for my own use as anyone else's.
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    (Original post by Zacken)
    4 lectures a day?! :eek:
    Yeah, that doesn't sound right in hindsight, sorry! Looking at lectured hours as posted by Gregorius, it looks like around 96 lectures in 8 weeks, so 12 lectures/term = 2 a day.
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    (Original post by DFranklin)
    Yeah, that doesn't sound right in hindsight, sorry! Looking at lectured hours as posted by Gregorius, it looks like around 96 lectures in 8 weeks, so 12 lectures/term = 2 a day.
    Okay, phew, that sounds more manageable but still quite strenuous.
 
 
 
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